A "change of basis" is an action performed in linear algebra, whereby a change in fundamental structure yields an entirely new viewpoint. This blog began as a record of a pedagogical change of basis for me, and continues as an ongoing account of my thoughts as I design and direct courses in mathematics at the University of North Carolina, Asheville.

Sunday, September 30, 2007

A rare conjunction of coursework came this weekend, and I found myself with four substantial assignments to grade over the last 48 hours. On Friday Calc I students submitted their sixth set of homework problems and their first team projects; 280 students turned in their fourth homework sets and their first take-home exams.

It took thirteen hours to grade it all: a couple of hours on Friday night, roughly eight hours yester(Satur)day, and another three this morning.

Highlights?

My first section of Calc I clocked in with their highest homework percentage yet.

The team project write-ups were uniformly good, with two or three exceptions, including one project that was so stellarly composed I felt it warranted a few extra points on top of the full measure. (This team was the only one of sixteen that had me look over a rough draft of their project before revising it to create the final version. I have two words for this team's leadership: "you," and "rock.")

The 280 exams were hit 'n' miss, the hits coming more frequently on the more difficult questions people spent the most time on ("Prove that every year has a Friday the 13th" and "obtain and prove carefully by induction a formula for the nth derivative of sin(x)"), the misses coming through careless errors in translating English propositions into quantifier notation. I'm hoping that with the opportunity to revise, students will be able to put a high shine on these rough drafts.

The 280 homework on induction was quite good, I think people are understanding the mechanics of an inductive proof pretty well. I've made a mental note, however, to spend a little bit of time tomorrow reminding them of the direction arrows must point when "reducing" the desired proposition to an "obvious" one. This tricky point was the number one cause of errors in the HW set.

The 280 folks are writing well. I'm much more conscious of the writing going on in the course this semester than I was last Spring, and I sense that the students are already stronger (or at least more self-conscious and self-aware) mathematical writers now than last year's students were by the semester's end.

Tomorrow?

Tomorrow, two of my departmental colleagues will be sitting in on my Foundations class in order to gather material to write letters on my behalf for the my reappointment file and for the teaching award for which I've been nominated. Woo hoo. I must say I'm sorry that it's nothing tremendously exciting we'll be discussing tomorrow, just some basic combinatorics (the Pigeonhole and Addition Principles, most likely). Too bad the committee reports won't come until Wednesday.